Rigged Hilbert space is considered the correct mathematical structure for quantum mechanics
Is it true that Rigged Hilbert space is considered the correct mathematical structure for quantum mechanics?
Yes. The retrieved literature supports the view that the rigged Hilbert space serves as a mathematically rigorous foundation for quantum mechanics, particularly by accommodating generalized eigenvectors and resolving limitations in standard Hilbert space formulations.
Verdict: SUPPORTED · 6 sources for, 0 against · Last checked
The claim asserts that the rigged Hilbert space is considered the correct mathematical structure for quantum mechanics. Multiple retrieved papers describe the rigged Hilbert space as providing a mathematically rigorous foundation that extends standard formulations and solves problems regarding resonances and decaying states. None of the provided papers refute this view, leading to a verdict of SUPPORTED.
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Böhm, A. (1981). Resonance poles and Gamow vectors in the rigged Hilbert space formulation of quantum mechanics. doi.org. https://doi.org/10.1063/1.524871
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Bohm, A. (1980). Decaying states in the rigged Hilbert space formulation of quantum mechanics. doi.org. https://doi.org/10.1063/1.524553
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Takahashi, J. & Ohmori, S. (2025). Rigged Hilbert Space Formulation of Quantum Thermo Field Dynamics and Mapping to Rigged Liouville Space..
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Schulte, C., Twarock, R., & Bohm, A. (1995). The Rigged Hilbert Space Formulation of Quantum Mechanics and its Implications for Irreversibility. arxiv.org. https://doi.org/10.48550/arXiv.9505004
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Takahashi, J. & Ohmori, S. (2025). Rigged Hilbert Space Formulation of Quantum Thermo Field Dynamics and Mapping to Rigged Liouville Space. arxiv.org. https://doi.org/10.48550/arXiv.2508.06923
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Bohm, A. & Harshman, N. L. (1998). Quantum Theory in the Rigged Hilbert Space-Irreversibility from Causality. arxiv.org. https://doi.org/10.1007/BFb0106783
- Is it true that Rigged Hilbert spaces provide the mathematical foundation for continuous spectra in quantum mechanics? SUPPORTED
- Is it true that Hilbert spaces provide the mathematical framework for quantum states and operators? SUPPORTED
- Is it true that quantum mechanics formulates physical observables as linear operators on Hilbert spaces? SUPPORTED
- Is it true that the Hamiltonian operator determines the Hilbert space of a quantum system? REFUTED
What does the evidence say?
The claim asserts that the rigged Hilbert space is considered the correct mathematical structure for quantum mechanics. Multiple retrieved papers describe the rigged Hilbert space as providing a mathematically rigorous foundation that extends standard formulations and solves problems regarding resonances and decaying states. None of the provided papers refute this view, leading to a verdict of SUPPORTED.
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